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Find a linear inequality with the following solution set. Each grid line represents one unit.

(Give your answer in the form \(ax+by+c>0\) or \(ax+by+c ≥0\) where \(a, b,\)  and \(c\) are integers with no common factor greater than 1.)

 

I don't understand how to input the answer so please help clarify for me!

 Nov 7, 2022
 #1
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The inequality is 3x - 7y > 1.

 Nov 7, 2022
 #2
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That's not right.

Keihaku  Nov 7, 2022
 #3
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The correct answer is -2x + 5y + 2 > 0.

 Nov 16, 2022
 #4
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That was also incorrect

Keihaku  Nov 16, 2022
 #5
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First consider the red dashed line.  The y-intercept is -1.  The slope is 2/1 = 2.

 

Therefore the equation of the line can be written as y = 2x - 1

 

The yellow region is below y, so the yellow region ca be expressed as  y < 2x - 1  

 

However, you are asked to exress it in the form ax + by + c >0, so subtract y from both sides of the previous equation to get 0 < 2x - y - 1

 

This is the same as  2x - y - 1 > 0

 

I've used > rather than >=, but if the yellow region is meant to include the red line then replace > by >=.

 Nov 17, 2022

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